Preheat a large grill pan over high heat until almost smoking.
Put the hot links split-side down on one side of the grill pan and grill over medium-high heat until some char marks appear, 4 to 5 minutes per side.
Meanwhile, brush the other side of the grill pan with canola oil. Add the onions and grill, tossing with tongs occasionally, until softened and golden brown, 10 to 15 minutes.
Add the garlic, paprika, cayenne and cloves to the onions and cook, stirring constantly, 1 minute.
Reduce the heat to low. Add the ketchup, brown sugar, vinegar, lemon juice, 1/3 cup water, 1 teaspoon salt and 1/2 teaspoon pepper and cook, stirring frequently to make sure the bottom doesn’t burn, until tender, 15 minutes.
Put the buns, split-side down, on the grill pan and grill until lightly toasted, 30 seconds per side.
Serve the hot links in the toasted buns, smothered with the barbecued onions.